Field of the Invention
The present invention relates to a mask pattern generation method and an optical image calculation method.
Description of the Related Art
In producing a semiconductor device using a photolithography technology, a projection exposure apparatus has been used which projects, through a projection optical system, a circuit pattern drawn on a mask (reticle) onto a substrate to transfer the circuit pattern to the substrate. In recent years, in accordance with miniaturization of semiconductor devices, a resolution enhancement technique to improve resolving power and depth of focus has been known.
As such a resolution enhancement technique, there has been a method for disposing an assist pattern (assist feature) for assisting the resolution of a target pattern, as well as the target pattern to be formed on a substrate, on a mask.
Japanese Patent Laid-Open Nos. 2004-221594 and 2008-40470 are typical examples of a method for designing an assist pattern on a mask. Japanese Patent Laid-Open No. 2004-221594 describes a method for disposing an assist pattern at a peak position (the position which takes an extreme value) of an interference map obtained by performing a Fourier transform of a first eigenfunction of a four-dimensional transmission cross coefficient (TCC). Japanese Patent Laid-Open No. 2008-40470 describes a method for obtaining an approximate aerial image using a two-dimensional transmission cross coefficient and disposing an assist pattern at a peak position of the approximate aerial image.
However, with the calculation methods using a transmission cross coefficient as described in Japanese Patent Laid-Open Nos. 2004-221594 and 2008-40470, a long calculation time may be required. Therefore, shortening of the calculation time has been demanded.